caa a22 4500 378936468 CHVBK 20180305123641.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0017 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0017 Variational and Finite Element Analysis of Vibroequilibria [Elektronische Daten] We adapt, via asymptotic expansion, Kapitsa's formula for the effective potential of a pendulum with vibrating suspension to rapidly forced potential flows with free boundaries. Determination of time-averaged stationary states leads to an optimal shape design problem. Under periodic boundary conditions existence and uniqueness of smooth minimizers to the averaged energy is proved using local coerciveness. In the numerical part of the article, 2D and 3D finite element approximations including related error estimates are discussed. Some illustrating examples are sketched. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. free boundary flows nationallicence timeaveraging nationallicence optimal shape design nationallicence finite element nationallicence Beyer K. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany. Günther M. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany. Timokha K. Institut für Angewandte Mathematik, Friedrich-Schiller-Universität, Ernst-Abbe-Platz 1-2, 07745 Jena, Germany. Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 290-323 1609-4840 4:3<290 2004 4 cmam https://doi.org/10.2478/cmam-2004-0017 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0017 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Beyer K. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany NATIONALLICENCE 700 1- Günther M. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany NATIONALLICENCE 700 1- Timokha K. Institut für Angewandte Mathematik, Friedrich-Schiller-Universität, Ernst-Abbe-Platz 1-2, 07745 Jena, Germany NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 290-323 1609-4840 4:3<290 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter